• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.517-529
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• 2012

In this paper, the existence theorem of two positive solutions is established for nonlinear m-point boundary value problem by using an inequality for the following third-order differential equations $$({\phi}(u^{\prime\prime}))^{\prime}+a(t)f(t,u(t))=0,\;t{\in}(0,1)$$, $${\phi}(u^{\prime\prime}(0))=\sum^{m-2}_{i=1}a_i{\phi}(u^{\prime\prime}({\xi}_i)),\;u^{\prime}(1)=0,\;u(0)=\sum^{m-2}_{i=1}b_iu({\xi}_i)$$, where ${\phi}:R{\rightarrow}R$ is an increasing homeomorphism and homomorphism and $\phi(0)=0$. The nonlinear term f may change sign, as an application, an example to demonstrate our results is given.

• Korean Journal of Computational Design and Engineering
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• v.1 no.1
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• pp.20-32
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• 1996

The boundary evaluation technique for Boolean operation on non-manifold models which is regarded as the most popular and powerful method to create and modify 3-D CAD models has been developed. This technique adopted the concept of Merge and Selection in which the CSG tree for Boolean operation can be edited quickly and easily. In this method, the merged set which contains complete information about primitive models involved is created by merging primitives one by one, then the alive entities are selected following the given CSG tree. This technique can support the hybrid representation of B-rep(Boundary Representation) and CSG(Constructive Solid Geometry) tree in a unified non-manifold model data structure, and expected to be used as a basic method for many modeling problems such as data representation of form features, and the interference between them, and data representation of conceptual models in design process, etc.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.183-194
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• 2009

In this paper, we considered the following four-point boundary value problem $\{{x"(t)+h(t)f(t,x(t),x'(t))=0,\;0<t<1\atop%20x'(0)=ax(\xi),\;x'(1)=bx(\eta)}\$. where $0\;<\;{\xi}\;<\;{\eta}\;<\;1,\;{\delta}\;=\;ab{\xi}\;-\;ab{\eta}\;+\;a\;-\;b\;<\;0,\;0\;<\;a\;<\;\frac{1}{\xi},\;0\;<\;b\;<\;\frac{1}{\eta}$. After the discussion of the Green function of the corresponding homogeneous system, we establish some criteria for the existence of positive solutions by using the generalized Leggett-William's fixed point theorem. The interesting point is the expression of the Green function, which is a difficulty for multi-point BVP.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.4 no.2
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• pp.46-53
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• 1995

In this study, Wear of a ceramic cutting tool for hardened STD11 steel was investigated. Under the finish machining condition. DOC notch wear of a ceramic cutting tool was mostly occurred earlier than flank and crater wear were proceeded. The relations of DOC notch wear, which was characteristically produced at the beginning of cutting. to cutting speed, feed, depth of cut, and nose radius of a ceramic cutting tool were examined. Effective approach angle, which is a function of cutting conditions, and boundary area were suggested, and then the influence of those was investigated, The following conclusions were obtained: (1)as cutting speed was increasing. DOC notch wear was decreasing (2) the cutting condition that magnitude of slendermess ratio was made small, was favorable for DOC notch wear, (3) as depth of cut was smaller, the influence of feed on DOC notch wear was also smaller, (4) DOC notch wear was mainly influenced by effective approach angle, but by boundary area in the range of low feed.

• Proceedings of the KIEE Conference
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• 1991.07a
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• pp.888-891
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• 1991

In this paper, we have shown a new approach of neural networks for mobile robot motion control under an indoor refracted environment. The vehicle has two powered wheels and four passive casters which support a free motion. And it also uses sonar sensors, infrared sensors, Internal odometer, and contact sensors. Two experiments were conducted to demonstrate our objectives. The first one is that the vehicle executes a reflexive motor control to maintain a constant distance to the boundary. The second one is that as well as the boundary following, the vehicle makes a block obstacle avoidance during its path. Without prior knowledge of external environment. we have accomplished the tasks by employing a simple, reactive stimulus-response neural network scheme associating sensor data with the vehicle's action.

• 한국가시화정보학회:학술대회논문집
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• 2005.12a
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• pp.117-120
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• 2005

This study of thermal convection uses the following geometry: a horizontal layer of fluid heated from below of solid lid at bottom and cooled from above. A variety range of thermal conductivity ratio, $\kappa$ is considered to investigate the interface temperature, $\theta_{i}$ between solid and fluid region. Periodic boundary conditions are employed in the horizontal direction to allow for lateral freedom for the convection cells. A two-dimensional solution for unsteady natural convection is obtained, using an accurate and efficient Chebyshev spectral multi-domain methodology, for different effective Rayleigh numbers, $Ra_{eff}$ varying over the range of $10^{4}\;to\;10^{7}$ in which the effective Rayleigh number is defined as $Ra{\times}<\overline{T}_{i}>$.

• International Journal of Aeronautical and Space Sciences
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• v.3 no.2
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• pp.76-81
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• 2002

A numerical simulation of wake behavior behind three-dimensional wings in ground effect is done using an indirect boundary element method (Panel Method). An integral equation is obtained by applying Green's 2nd Identity on all surfaces of the flow domain. The AIC is constructed by imposing the no penetration condition on solid surfaces, and the Kutta at the wing's trailing edge. The ground effect is included using an image method. At each time step, a row of wake panels from wings' trailing edge are convected downstream following the force-free condition. The roll-up of wake vortices behind wings in close proximity is simulated.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.227-274
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• 2001

In this paper we intended to discuss the following topics: (1) Notation, generalities, Markov processes. The close relationship between (generators of) Markov processes and the martingale problem is exhibited. A link between the Korovkin property and generators of Feller semigroups is established. (2) Feynman-Kac semigroups: 0-order regular perturbations, pinned Markov measures. A basic representation via distributions of Markov processes is depicted. (3) Dirichlet semigroups: 0-order singular perturbations, harmonic functions, multiplicative functionals. Here a representation theorem of solutions to the heat equation is depicted in terms of the distributions of the underlying Markov process and a suitable stopping time. (4) Sets of finite capacity, wave operators, and related results. In this section a number of results are presented concerning the completeness of scattering systems (and its spectral consequences). (5) Some (abstract) problems related to Neumann semigroups: 1st order perturbations. In this section some rather abstract problems are presented, which lie on the borderline between first order perturbations together with their boundary limits (Neumann type boundary conditions and) and reflected Markov processes.

• Korean Journal of Mathematics
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• v.16 no.1
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• pp.41-49
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• 2008

We show the existence of a negative solution for the system of the following nonlinear wave equations with critical growth, under Dirichlet boundary condition and periodic condition $$u_{tt}-u_{xx}=au+b{\upsilon}+\frac{2{\alpha}}{{\alpha}+{\beta}}u_+^{\alpha-1}{\upsilon}_+^{\beta}+s{\phi}_{00}+f,\\{\upsilon}_{tt}-{\upsilon}_{xx}=cu+d{\upsilon}+\frac{2{\alpha}}{{\alpha}+{\beta}}u_+^{\alpha}{\upsilon}_+^{{\beta}-1}+t{\phi}_{00}+g,$$ where ${\alpha},{\beta}>1$ are real constants, $u_+={\max}\{u,0\},\;s,\;t{\in}R,\;{\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}$ of the wave operator and f, g are ${\pi}$-periodic, even in x and t and bounded functions.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.355-362
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• 2008

We prove the existence of a unique positive solution for a class of systems of the following nonlinear suspension bridge equation with Dirichlet boundary conditions and periodic conditions $$\{{u_{tt}+u_{xxxx}+\frac{1}{4}u_{ttxx}+av^+={\phi}_{00}+{\epsilon}_1h_1(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,\\{v_{tt}+v_{xxxx}+\frac{1}{4}u_{ttxx}+bu^+={\phi}_{00}+{\epsilon}_2h_2(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,$$ where $u^+={\max}\{u,0\},\;{\epsilon}_1,\;{\epsilon}_2$ are small number and $h_1(x,t)$, $h_2(x,t)$ are bounded, ${\pi}$-periodic in t and even in x and t and ${\parallel} h_1{\parallel}={\parallel} h_2{\parallel}=1$. We first show that the system has a positive solution, and then prove the uniqueness by the contraction mapping principle on a Banach space